The mean score for a standardized test is 1700 points. The results are normally distributed with a standard deviation of 75 points. If 10,000 students take the exam, how many would you expect to score between 1700 and 1775 points?

1 Answer
Shwetank Mauria
Feb 25, 2018

Expected number of students, out of #10000# students, scoring a score between #1700# and #1750# is #2475#.

Explanation:

We have to find expected number of students (out of #10000# students), scoring a score between #1700# and #1750#. This is #10000# multiplied by the probability of scoring between #1700# and #1775# points given that distribution is normally distributed, with mean score of #1700# and standard deviation of #75# points.

Let us first calculate #z#-score for #1700# and #1775#. #z#-score for #1700# is #(1700-1700)/75=0# and for #1775# it is #(1750-1700)/75=50/75=0.6667#.

Hence probability of scoring between #1700# and #1775# points from tables is #0.2475#. (For more details see here. .)

Hence, expected number of students (out of #10000# students), scoring a score between #1700# and #1750# is #0.2475xx10000=2475#.

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